Question

A sprinkler set in the middle of a lawn sprays in a circular pattern. The area of the lawn that gets sprayed by the sprinkler

can be described by the equation (z+6)2 + (y-9)² = 196.
What is the greatest distance, in feet, that a person could be from the sprinkler and get sprayed by it?

Answer 1

Answer: The greatest distance a person could be from the sprinkler and get sprayed by it is 14 feet.

Explanation:

The equation given describes a circle with the general equation (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

In the provided equation, (z + 6)^2 + (y - 9)^2 = 196, we can identify the values for h, k, and r^2:

1. h = -6 (from z + 6)

2. k = 9 (from y - 9)

3. r^2 = 196

Now, we need to find the radius r, which is the greatest distance a person could be from the sprinkler and still get sprayed by it. To do this, we take the square root of r^2:

r = √196

r = 14